Unformatted text preview: with a mean of 50. If the variance of the r.v. is known to be 25, then what is a lower bound on the probability that this week’s production will be between 40 and 60? 4. Problem 81, page 182. 5. A voltage V is a function of time t and is given by V ( t ) = X cos(2 πft )+ Y sin(2 πft ) , in which f is the frequency (in Hz) and X and Y are two independent Gaussian zero mean r.v.’s of variance σ 2 . a. Show V ( t ) can be written as V ( t ) = R cos(2 πft-Θ) . Hint: deﬁne R = ( X 2 + Y 2 ) . 5 . b Show R is a Rayleigh r.v. and Θ is uniformly distributed in [0 , 2 π ) , and these two r.v.’s are independent. 6. Problem 22, page 320. Hint: Use CLT and Gaussain r.v. to approximate the Binomial r.v....
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- Spring '08
- Probability theory, Rayleigh, K. Yao, 16th Read pp, ﬁrst door